I can only say that the arrangement shown in the photograph is one possible way to construct a condenser microphone capsule--with the center of its diaphragm used as one of the points of electrical contact (thus forcing the center to hold still relative to the backplate--from which it is of course insulated by a spacer that you can't see in the picture), instead of using the edge of the diaphragm as the electrical contact and allowing the center to move more freely. (Please note the word "more" ...) It is neither a better nor a worse way of doing things.
Of course a diaphragm will vibrate somewhat differently when its center can't move. But the capacitance of the capsule will still vary, in general, proportionally to the excursion caused by sound energy that strikes it. And the diaphragm of a condenser microphone never moves very far in response to sound energy anyway--even when the center is more free to move (there's that relative word again ...) and the sound is extremely loud.
If you take just the diaphragm and the ring that holds it under tension, and separate it from the backplate and the rest of the capsule, you could tap the diaphragm with your finger and produce a tiny sound which would (if the diaphragm has been properly tensioned) have one main resonant frequency plus other, subsidiary resonances. But any finished capsule as a whole must smooth out ("damp") those resonances for the most part--otherwise the capsule would have only a narrow frequency range, and any sounds near its resonant frequencies would "ring" (= continue longer than other frequencies, even after the stimulus stops) each time they occurred in actual sound.
This is why there is always an air chamber behind the backplate, with holes drilled through the backplate to allow the space in front of the diaphragm to "communicate" with the space behind it--even in an omni (pressure transducer), where that rear chamber is sealed off from the outside world. The air behind the diaphragm thus undergoes some friction whenever the diaphragm moves forward or backward. The air has some springiness of course, and the tensioned diaphragm has some elasticity as well. But the friction limits and controls the motion of the air behind the diaphragm, damping the resonances to a very precisely determined degree across the frequency spectrum. The size and placement of those holes form a major part of what gives each microphone its distinct sonic characteristics.
In summary, a diaphragm should never be thought of as an independent "free agent" that is "allergic" to anything that might control or limit its motion. It has a specific role to play in the totality of the capsule's acoustic design, and it plays that role in a way that is greatly influenced--constrained--by the capsule's interior air spaces and passageways. So the center contact point is simply one more thing that limits the diaphragm's motion in this case. It has some effect on the result, but not as much as other design factors have.
P.S.: Maybe the word "backplate" confuses people--in German the word is "Gegenelektrode" (= "opposite electrode") which expresses its electrical function alone. But its mechanical/acoustical function is not to be the "back" of the capsule as a whole; it's really more like the middle of it, in a front-to-back sense.
Backplates may also have indentations or grooves that don't go through to the other side. Such refinements contribute to the frequency and time-domain response of the capsule, again influencing the motion of the diaphragm by influencing the air motion in the space behind it.
--I've been describing capsules as if they always have only one diaphragm and backplate, whereas in many designs (though not in the kinds of microphones that I would say are are generally best suited for the kinds of recording that most people here do most of the time) there is a symmetrical arrangement of two back-to-back diaphragms and backplates. Such designs are more complicated in the way they work acoustically, but the basic principles are the same.